Balanced Contributions in Networks and Games with Externalities
TLDR
This paper introduces the unique Balanced Contributions and Component-Efficient (BCE) rule for allocating value in networks with externalities.
Key contributions
- Introduces and characterizes the unique Balanced Contributions and Component-Efficient (BCE) allocation rule.
- Overcomes existence challenges for the BCE rule using a novel cycle-sum identity.
- Demonstrates the BCE rule generalizes the Myerson value and Jackson-Wolinsky values.
- Distinguishes the BCE rule from fairness-based FCE rules in network games.
Why it matters
This paper provides a foundational allocation rule for networks with complex interdependencies. The BCE rule offers a unique, component-efficient solution that generalizes existing concepts, making it crucial for understanding value distribution in systems with externalities.
Original Abstract
For networks with externalities, where each component's worth may depend on the full network structure, balanced contributions and fairness lead to distinct component-efficient allocation rules. We characterize the unique component-efficient allocation rule satisfying balanced contributions -- the BCE rule. Existence is the main challenge: balanced contributions must hold on every edge, but the construction uses only spanning-tree edges. A cycle-sum identity bridges this gap by reducing balanced contributions on non-tree edges to relations in proper subnetworks. The BCE rule coincides with the Myerson value for TU games and with its generalization by Jackson--Wolinsky for network games without externalities, it recovers the externality-free value on the complete network, and -- unlike the fairness-based FCE rule -- it does not reduce to a graph-free formula applied to the graph-restricted game.
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